Determining physical properties inside an object without access to direct measurements of target regions can be formulated as a specific type of \textit{inverse problem}. One of such problems is applied in \textit{Electrical Impedance Tomography} (EIT). In general, EIT can be posed as a minimization problem and solved by iterative methods, which require knowledge of derivatives of the objective function. In practice, this can be challenging because analytical closed-form solutions for them are hard to derive and implement efficiently. In this paper, we study the effectiveness of \textit{automatic differentiation (AD)} to solve EIT in a minimization framework. We devise a case study where we compare solutions of the inverse problem obtained with AD methods and with the manually-derived formulation of the derivative against the true solution. Furthermore, we study the viability of AD for large scale inverse problems by checking the memory and load requirements of AD as the resolution of the model increases. With powerful infrastructure, AD can pave the way for faster and simpler inverse solvers and provide better results than classical methods.

翻译：确定物体内部无法直接测量目标区域的物理性质可被建模为特定类型的\textit{逆问题}。此类问题之一应用于\textit{电阻抗层析成像}（EIT）。通常，EIT可表述为最小化问题并通过迭代方法求解，这需要目标函数导数的知识。在实践中，这一过程可能具有挑战性，因为其解析闭式解难以推导并高效实现。本文研究了\textit{自动微分（AD）}在最小化框架中求解EIT的有效性。我们设计了一个案例研究，将使用AD方法获得的逆问题解与手动推导的导数公式所得解进行对比，并评估其与真实解的接近程度。此外，我们通过检查随模型分辨率增加时AD的内存和负载需求，研究了AD用于大规模逆问题的可行性。借助强大的基础设施，AD可为更快速、更简单的逆求解器铺平道路，并提供优于经典方法的结果。